The invention finds interesting applications in telephony devices satisfying the DECT standard. The invention also shows interest in the standards which impose a permanent search for idle channels, so that an idle channel is to be found quickly without this being noticed too much by the user. However, this monitoring of channels implies the use of electronic circuits which consume electric energy and therefore this channel monitoring reduces the autonomy of the handsets which are usually supplied with power by an accumulator. Furthermore, the DECT standards impose that a requested channel search be made in the 30s prior to a request for a channel link.